President Donald Trump has suspended the US green card lottery scheme in the wake of a mass shooting at Brown University last week in which two people were killed.

The suspect, a Portuguese man who was found dead on Thursday, entered the country through the diversity lottery immigrant visa programme (DV1) in 2017 and was granted a green card.

Homeland Security Secretary Kristi Noem said she has paused the visa scheme under Trump's direction to ensure no more Americans are harmed by this disastrous programme.

US officials said they believe the suspect, 48-year-old Claudio Neves Valente, also killed Portuguese Massachusetts Institute of Technology professor Nuno Loureiro earlier this week.

The programme makes up to 50,000 visas available each year through a random selection process among entries from countries with low rates of immigration to the US.

Writing on social media, Noem said Trump had previously fought to end the scheme in 2017 after eight people were killed in a truck-ramming attack in New York City.

Uzbekistan national Sayfullo Saipov, an Islamic State supporter who is serving multiple life sentences for the attack, entered the US through the DV1 scheme, according to Noem.

Her comments come just hours after Neves Valente was found dead in a storage facility in Salem, New Hampshire, from what police believe is a self-inflicted gunshot wound.

Police said video evidence and tips from the public led investigators to a car rental location where they found the suspect's name and matched him to their person of interest, following a six-day multi-state manhunt.

He was found dead with a satchel and two firearms. Evidence in a car nearby matched to the scene of the shooting at Brown University in Providence, according to Rhode Island Attorney General Peter Neronha.

Brown University President Christina Paxson said Neves Valente was enrolled at the Ivy League school from the autumn of 2000 to the following spring, studying for a PhD in physics. He had no current active affiliation to Brown.

Officials also reported that Neves Valente shot and killed MIT professor Nuno F Gomes Loureiro, 47, on Monday at his home in Brookline, about 50 miles from Providence.

Both men had studied at the same university in Portugal in the late 1990s.

Authorities have yet to establish a motive for either of the shootings, which left two students dead and several others injured during finals week at Brown University.